Chapter 2, Problem 2.63UTC

In which of the fo1losing pairs do both numbers contain the same number of significant figures? (2.2)

a. 2.0500 m and 0.0205 m
b. 600.0 K and 60 K
c. 0.000 75 s and 75 000 s
d. 6.240 L and $\text{6}\text{.24}0\text{×1}{0}^{-2}$ L

Interpretation Introduction

To determine:

The pairs of numbers that contain the same number of significant figures

Answer to Problem 2.63UTC

c) 0.000 75 s and 75 000 s

d) 6.240 L and 6.240 × 10-2 L

Explanation of Solution

A number is significant if it is:

• Non-zero digit.
• Any zeros between two or more non-zero digits.
• Trailing zeroes in the decimal number.

Also, note that zero placed after a non-zero digit without any decimal is simply a place holder and insignificant. Therefore, as per the above rules one can write:

a)

Number	Significant Figures
2.0500 m	5
0.0205 m	3

b)

Number	Significant Figures
600.0 K	4
60 K	1

c)

Number	Significant Figures
0.000 75 s	2
75 000 s	2

d)

Number	Significant Figures
6.240 L	4
6.240 × 10-2 L	4

Conclusion

The pairs of numbers in (c) and (d) have the same significant figures.